A different research direction focuses on training neural networks with physics constrained optimization [1]}, [2]}. These method use Automatic Differentiation (AD) [3]} to compute PDE derivatives. The physics-based approaches have been extended to solve complicated PDEs representing complex physics [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}. More recently, alternate approaches that use discretization techniques using higher order derivatives and specialize numerical schemes to compute derivatives have shown to provide better regularization for faster convergence [22]}, [23]}, [24]}, [25]}. However, the use of optimization techniques to solve PDEs, although accurate, has proved to be extremely slow as compared to traditional solvers and hence, non-scalable to high resolution meshes.
